Solve for $x$ and $y$ using elimination. ${x+2y = 12}$ ${-x+3y = 3}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $5y = 15$ $\dfrac{5y}{{5}} = \dfrac{15}{{5}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {x+2y = 12}\thinspace$ to find $x$ ${x + 2}{(3)}{= 12}$ $x+6 = 12$ $x+6{-6} = 12{-6}$ ${x = 6}$ You can also plug ${y = 3}$ into $\thinspace {-x+3y = 3}\thinspace$ and get the same answer for $x$ : ${-x + 3}{(3)}{= 3}$ ${x = 6}$